MathDB

B1

Part of 1964 Putnam

Problems(1)

Putnam 1964 B1

Source: Putnam 1964

3/5/2022
Let uku_k be a sequence of integers, and let VnV_n be the number of those which are less than or equal to nn. Show that if ∑k=1∞1uk<∞,\sum_{k=1}^{\infty} \frac{1}{u_k } < \infty, then lim⁡n→∞Vnn=0.\lim_{n \to \infty} \frac{ V_{n}}{n}=0.
PutnamConvergence